Mesoscopic Physics

Simons, Ben; Altland, Alexander

doi:10.1007/978-1-4757-3671-7_6

Cited by 8 publications

(9 citation statements)

References 117 publications

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“…In the quasi-classical limit ǫ F τ ≫ 1, where 1/τ represents the scattering rate of the non-magnetic impurity distribution, the spectral and transport properties of the weakly disordered system can be presented in the framework of a statistical field theory of non-linear σ-model type (for a review see, e.g. [10]). Within this approach, the conventional Abrikosov-Gor'kov meanfield theory is identified as the set of (homogeneous) saddle-point equations.…”

Section: Beyond Mean-field Theorymentioning

confidence: 99%

“…The homogeneous saddle-point solutions are given by the values of u satisfying Eq. (10). As in the Abrikosov-Gor'kov theory, a number of features of the DoS can be deduced starting from the shape of the function g(u, ζ, α) when the impurity concentration ζ and the scattering amplitude α are varied.…”

Section: Low-energy Saddle-pointmentioning

confidence: 99%

“…In order to explicitly find ν mf (ǫ) V,S /ν, we have to solve equation (10), expressing u in terms of ǫ/|∆|. For values of α and ζ at which all the edges, ǫ g /|∆| = Φ 1 , Φ 2 and Φ 3 are different from zero, equation (10) has complex solutions for Φ 1 < ǫ/|∆| < Φ 2 and for ǫ/|∆| > Φ 3 .…”

Section: Low-energy Saddle-pointmentioning

confidence: 99%

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Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Marchetti¹,

Simons²

2002

J. Phys. A: Math. Gen.

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When subject to a weak magnetic impurity distribution, the order parameter and quasi-particle energy gap of a weakly disordered bulk s-wave superconductor are suppressed. In the Born scattering limit, recent investigations have shown that 'optimal fluctuations' of the random impurity potential can lead to the nucleation of 'domains' of localised states within the gap region predicted by the conventional Abrikosov-Gor'kov mean-field theory, rendering the superconducting system gapless at any finite impurity concentration. By implementing a field theoretic scheme tailored to the weakly disordered system, the aim of the present paper is to extend this analysis to the consideration of magnetic impurities in the unitarity scattering limit. This investigation reveals that the qualitative behaviour is maintained while the density of states exhibits a rich structure.

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Section: Beyond Mean-field Theorymentioning

confidence: 99%

Section: Low-energy Saddle-pointmentioning

confidence: 99%

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Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Marchetti¹,

Simons²

2002

J. Phys. A: Math. Gen.

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“…With this background, let us now turn to the construction of a field theory to describe statistical correlations of the non-Hermitian model. Motivated by the correspondence outlined above, the analysis will parallel previous investigations of the weakly disordered superconductor [37,38,39]. The starting point is the generating functional for the singleparticle Green function.…”

Section: Generating Functionalmentioning

confidence: 99%

Optimal fluctuations and tail states of non-Hermitian operators

Marchetti

Simons²

2001

J. Phys. A: Math. Gen.

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A statistical field theory is developed to explore the density of states and spatial profile of 'tail states' at the edge of the spectral support of a general class of disordered non-Hermitian operators. These states, which are identified with symmetry broken, instanton field configurations of the theory, are closely related to localized sub-gap states recently identified in disordered superconductors. By focusing separately on the problems of a quantum particle propagating in a random imaginary scalar potential, and a random imaginary vector potential, we discuss the methodology of our approach and the universality of the results. Finally, we address potential physical applications of our findings.

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“…The NLSM is a quantum field theory 25 of weakly disordered mesoscopic conductors where diffusion modes of the diagrammatic perturbation theory play the role of soft modes responsible for long-range spatial correlations of local density of states, mesoscopic fluctuations of global quantities, and nonlocal corrections to conductivity. 34 It makes it possible to handle the breakdown of perturbation theory due to the proliferation of such modes 34 by summarizing all WL-type corrections to conductivity. 30 This then justifies the phenomenological one-parameter scaling theory 7 (if not rigorously, then at least qualitatively), and explains the LD transition in 2 + ǫ dimensions where Anderson localization occurs at weak disorder k F ℓ ≫ 1.…”

Section: 31mentioning

confidence: 99%

Deconstructing Kubo formula usage: Exact conductance of a mesoscopic system from weak to strong disorder limit

Nikolić

2001

Phys. Rev. B

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In both research and textbook literature one often finds two "different" Kubo formulas for the zerotemperature conductance of a non-interacting Fermi system. They contain a trace of the product of velocity operators and single-particle (retarded and advanced) Green operators: Tr(vxĜ rv xĜ a ) or Tr(vx ImĜvxImĜ). The study investigates the relationship between these expressions, as well as the requirements of current conservation, through exact evaluation of such quantum-mechanical traces for a nanoscale (containing 1000 atoms) mesoscopic disordered conductor. The traces are computed in the semiclassical regime (where disorder is weak) and, more importantly, in the nonperturbative transport regime (including the region around localization-delocalization transition) where concept of mean free path ceases to exist. Since quantum interference effects for such strong disorder are not amenable to diagrammatic or nonlinear σ-model techniques, the evolution of different Green function terms with disorder strength provides novel insight into the development of an Anderson localized phase.PACS numbers: 72.10. Bg, 72.15.Rn, 05.60.Gg At first sight, the title of this paper might sound perplexing. What else can be said about Kubo formula 1 after almost a half of a (last) century of explorations in practice, as well as through numerous re-derivations in both research 2 and textbook 3,4 literature? Kubo linear response theory (KLRT) represents the first full quantum-mechanical transport formalism. It connects irreversible processes in nonequilibrium to the thermal fluctuations in equilibrium [fluctuation-dissipation theorem (FDT)]. Therefore, the study of transport is limited to the nonequilibrium states close to equilibrium. Nevertheless, the computation of linear kinetic coefficients is greatly facilitated since final expressions deal with equilibrium expectation values of relevant physical quantities (which are much simpler than the corresponding nonequilibrium ones 5 ). It originated 6 from the Einstein relation for the diffusion constant and mobility of a particle performing a random walk.Until the scaling theory of localization, 7 and ensuing computation of the lowest order quantum correction, weak localization 8 (WL), to the Drude conductivity, it almost appeared that microscopic and complicated Kubo formulation of quantum transport merely served to justify the intuitive Bloch-Boltzmann semiclassical approach 3 to transport in weakly disordered (k F ℓ ≫ 1, k F is the Fermi wave vector and ℓ is the mean free path) conductors. Furthermore, the advent of mesoscopic physics 9 has led to reexamination of major transport ideas-in particular, we learned how to apply properly KLRT to finite-size systems. Thus, the equivalence was established 2 between the rigorous Kubo formalism and heuristically founded Landauer-Büttiker 10 scattering approach to linear response transport of non-interacting quasiparticles.11 This has emerged as an important tool in for studying mesoscopic transport phenomena, where system size and interface...

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Mesoscopic Physics

Cited by 8 publications

References 117 publications

Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Tail states in disordered superconductors with magnetic impurities: the unitarity limit

Optimal fluctuations and tail states of non-Hermitian operators

Deconstructing Kubo formula usage: Exact conductance of a mesoscopic system from weak to strong disorder limit

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